Many schools are satisfied to let children coast along, it is sad but inevitable I suppose.
I would advise teaching him by stealth. What subjects does he really like? See if you can help him dig deeper. Try to engage him in conversation daily about what he learned at school, and find ways to make it relevant and extend his knowledge at home. There are some fantastic series on YouTube, on all sorts of subject areas. You could also buy some second hand books on subjects he is interested in. What does he really like?
eg if he likes maths and science, get him to help you in the kitchen, weighing out ingredients - the recipe asks for 55g but you are doing double the recipe, can he work out how much you need? Get him to estimate and predict - is a tbs of flour going to weigh more than a tbs of water? Make a cake and talk about melting and boiling points and states of matter. Get him to cut up a pizza and do some work on adding fractions and simplifying fractions.
Puzzle books are also a good idea - sudoku, crosswords, word searches etc.
And obviously read, read, read - non fiction as well as fiction. This could be online too eg children's news websites, National Geographic, the European Space Agency, whatever you like.
Encourage him to write at home - he can do your shopping lists, write the Christmas cards and thank you letters. He might like to write stories, or make his own comic, or write a script for an animation he can record with his Lego figures.
Drilling him through books and worksheets at home, when he isn't being set the work by school, is going to seem like a punishment. Far better to really engage him and self motivate.
One area where you should focus is spelling, as it is tested as part of the "working above standard". You can find the statutory spellings for y3/Y4 online, and ditto for the y5/y6 spellings. There are some great resources for spelling - spellingframe is particularly good as it is game based and you can set up customs lists as well as using pre-determined lists.